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The circuit starts in an equal superposition over m=n−1 partition bits, then alternates a diagonal phase depending on the cost and a mixing rotation generated by Pauli X operators. Depth p counts these alternating layers, and the angles are classically optimized. The experiment simulates p=1 and p=2 with a dense exact statevector and exhaustive cost table, so its output-quality results do not demonstrate a computational speedup.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| psi_p | State after p layers |
| beta | Mixer angles |
| gamma | Cost angles |
| H_C | Diagonal normalized-and-penalized cost operator |
| X_q | Pauli X on bit q |
| m | n−1 encoded bits |
How it works
Use m=n−1 binary variables for a cut after fixing one vertex to remove complementary duplicates.
Prepare |+⟩⊗m, the equal-amplitude quantum state over those bit strings; ket bars name a state vector, not an absolute value.
Apply the diagonal cost unitary exp(−iγ_l H_C), which changes relative complex phases according to each cut’s cost.
Apply the Pauli-X mixer exp(−iβ_l ΣX_q), then repeat for the stated p layers in the source’s convention.
Optimize the angles classically and sample bit strings from squared amplitudes. The recovered experiment simulates the state vector and uses an already exhaustive cost table.
Assumptions & limits
Source recovery establishes that the expression appears in this record. Its mathematical validity, implementation behavior, and interpretation must be assessed separately. See the linked source and research notes for the checks available for this version.
Original context
Read the surrounding source passage
Each of ten independent runs per network uses four random restarts and 512 single-bit proposals per restart. Metropolis acceptance is $\min\{1,e^{-\Delta J/T}\}$. Temperature decreases geometrically from $T_0$ to $10^{-3}T_0$, with $T_0=\max\{\operatorname{SD}(32\text{ random pilot scores}),0.001\}$. All-in-one proposals are rejected and consume a proposal step. The best visited valid partition, including pilot points, is retained. Each run uses a fresh cached oracle; it receives neither the optimum nor the reference table. Maximum budget: 2,048 proposals plus 36 pilot/initial evaluations.
[Context excerpt; full source linked.]Exact original notation
|\psi_p\rangle=\prod_{\ell=1}^{p}
e^{-i\beta_\ell\sum_{q=1}^{m}X_q}e^{-i\gamma_\ell H_C}|+\rangle^{\otimes m},
\quad p\in\{1,2\}.Related builds
Sources & provenance
|\psi_p\rangle=\prod_{\ell=1}^{p} e^{-i\beta_\ell\sum_{q=1}^{m}X_q}e^{-i\gamma_\ell H_C}|+\rangle^{\otimes m}, \quad p\in\{1,2\}.
|\psi_p\rangle=\prod_{\ell=1}^{p} e^{-i\beta_\ell\sum_{q=1}^{m}X_q}e^{-i\gamma_\ell H_C}|+\rangle^{\otimes m}, \quad p\in\{1,2\}.